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Number of 3 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
1

%I #10 Sep 12 2018 15:08:53

%S 4,8,39,126,482,1712,6277,22700,82580,299648,1088499,3952186,14352786,

%T 52119040,189266297,687294648,2495834292,9063317432,32912374319,

%U 119517358582,434013128786,1576067091632,5723300581661,20783486354532

%N Number of 3 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.

%H R. H. Hardin, <a href="/A228755/b228755.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-4).

%F Empirical g.f.: x*(2 - x)*(2 + x) / (1 - 2*x - 6*x^2 + x^4). - _Colin Barker_, Sep 12 2018

%e Some solutions for n=4:

%e ..1..0..0..0....1..0..1..0....1..0..0..1....1..0..0..0....1..0..1..0

%e ..1..0..1..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..1

%e ..0..0..0..0....0..1..0..1....0..1..0..1....0..1..0..0....1..0..0..1

%Y Row 3 of A228754.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 02 2013